Multivariate Nonnegative Quadratic Mappings

CentER Discussion Paper No. 2003-07

28 Pages Posted: 14 May 2004

See all articles by Zhi-Quan Luo

Zhi-Quan Luo

University of Minnesota - Twin Cities - Electrical and Computer Engineering

Shuzhong Zhang

The Chinese University of Hong Kong (CUHK) - Faculty of Engineering

Jos F. Sturm

Tilburg University - CentER

Date Written: January 2003

Abstract

In this paper we study several issues related to the characterization of specific classes of multivariate quadratic mappings that are nonnegative over a given domain, with nonnegativity defined by a pre-specified conic order. In particular, we consider the set (cone) of nonnegative quadratic mappings de ned with respect to the positive semidefinite matrix cone, and study when it can be represented by linear matrix inequalities. We also discuss the applications of the results in robust optimization, especially the robust quadratic matrix inequalities and the robust linear programming models. In the latter application the implementational errors of the solution is taken into account, and the problem is formulated as a semidefinite program.

Keywords: Linear Matrix Inequalities, Convex Cone, Robust Optimization, Bi-Quadratic Functions

Suggested Citation

Luo, Zhi-Quan and Zhang, Shuzhong and Sturm, Jos F., Multivariate Nonnegative Quadratic Mappings (January 2003). CentER Discussion Paper No. 2003-07. Available at SSRN: https://ssrn.com/abstract=545582 or http://dx.doi.org/10.2139/ssrn.545582

Zhi-Quan Luo (Contact Author)

University of Minnesota - Twin Cities - Electrical and Computer Engineering

Duluth, MN 55812
United States

Shuzhong Zhang

The Chinese University of Hong Kong (CUHK) - Faculty of Engineering ( email )

Ho Sin Hang Engineering Building, Room 228
Shatin, N.T.
Hong Kong
852 2609 8240 (Phone)
852 2603 5505 (Fax)

HOME PAGE: http://www.se.cuhk.edu.hk/~zhang/

Jos F. Sturm

Tilburg University - CentER ( email )

Postbus 90153
Tilburg, DC 5000 LE
Netherlands

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